Material Models in SCC Mix Design

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Material Models in SCC Mix Design

Claus Pade, SCC-seminar in Copenhagen, 19 June, 2006



Types of Model

Emperic

- Too simplistic

- It works but you don’t know why

Analytic

- Too complicated

- It works and you know why



Danish SCC-Consortium Model

ϕ

ϕ ϕ

⋅

−=Γ

k f

*1

Originally proposed by Oh et al.:

1+Γ⋅= −

η

η η η

B

pasteconcrete A

1,0,0 +Γ⋅= −

τ

τ τ τ

B

pasteconcrete A

ηconcrete , is the plastic viscosity of the

concrete

ηpasta , is the plastic viscosity of the paste

τ0,concrete , is the yield stress of the concrete

τ0,pasta , is the yield stress of the paste

Aη, A

τ, B

η, B

τ, are constants

Γ, is the relative thickness of excess paste

φ, is the volume fraction of the aggregate

φ*, is the max volume fraction of the

aggregate

f/k, is a shape factor – related to the ratio

between surface and volume of a particlewith characteristic dimension 1

f/k (sphere) = 6

f/k > 6 for all other shapes



Elements of the Model

Excess paste

D

R

Γ = R/D is the same for

either particle

The excess of paste is found

around each aggregate

particle with Γ = R/Dconstant for all aggregate

particles



Experimental Program

1,0,0 +Γ⋅= −

τ

τ τ τ

B

pasteconcrete Aϕ

ϕ ϕ

⋅

−=Γ

k f

*1

τ0,paste

η paste

EMPA Zürich - Estimated from plate-plate rheological measurements

φ*

φ/φ*

DTI - Estimated using the 4C Packing software

f/k

A

B

Fit-parameters in regression analysis

τ0,concrete

ηconcreteDTI - Estimated using 4C Auto Slump Flow equipment



Materials and Composition

0/4 4/8 8/16

Natural pit Crushed granite Crushed granite

Max packing

w/c

SP-konc

Excess paste

0.35

0.50

160,170,180,190 L

Mix 3

0.804

Identical pastes in all three mixtures

0/2 4/8 8/16

Natural pit Sea dredged Sea dredged

Max packing

w/c

SP-konc

Excess paste

Mix 1

0.808

0.35

0.50

110,120,130,140 L

0/2 4/8 8/16

Glass beads Glass beads Glass beads

Max packing

w/c

SP-konc

Excess paste

0.848

0.35

0.50

100,110,120,130 L

Mix 2



4C Packing Diagrams

8/16

4/8

0/4

8/16

8/16

0/4

0/4

4/8

4/8

37,18,45, 0.80837,18,45, 0.848

45,10,45, 0.804



4C Auto Slump Flow

Yield stress = 26 Pa

Plastic viscosity = 44 Pa x s

Time (s)

S l u m

p f l o w

s p r e a d ( m m )

—— Best fit

—— Eksperiment



Results – Yield Stress

0

25

50

75

100

125

150

175

200

0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94

phi/phi*

Y i e l d s t r e s s (

P a )

Shapefactor = 11.7 Shapefactor = 6

Shapefactor = 7

3.46

,0 105.4 −−Γ××=concreteτ

ϕ

ϕ ϕ

⋅

−=Γ

r shapefacto

*1

φ /φ*



Results – Yield Stress

0

20

40

60

80

100

120

140

160

180

200

0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80

Aggregate volume fraction

Y i

e l d S t r e s s ( P a )

50 Pa

Crushed Natural Glass beads

Crushed +100L excess pasteNatural +45L excess paste

φ,



0

2

4

6

8

10

12

14

16

8 / 1 6 s e

a d r e d

g e d

4 / 8 s e

a d r e d

g e d

4 / 8 c r u s h e

d I

2 / 8 c r u s h e

d I I

8 / 1 6

c r u s h

e d I

G l a

s s 1 4 m

m

G l a

s s 6 m m

B o t t o m

a s h

S

h a p e f a c t o r

Shapefactor – Image Analysis

Parameter guess Parameter measurement



0

2

4

6

8

10

12

14

16

0 / 2 n a

t u r a l p

i t

0 / 4 n a

t u r a l p

i t

G l a

s s 0 / 4

S h

a p e f a c t o r

Shapefactor – Image Analysis

Parameter guess Parameter measurement



Status

Estimate particle packing parameter - φ* OK!

Select aggregate proportions – φ OK!

Estimate shapefactor ?

Estimate the constants A and B ?

1,0,0 +Γ⋅= −

τ

τ τ τ

B

pasteconcrete Aϕ

ϕ ϕ

⋅

−=Γ

k f

*1

B

concrete A Γ×=,0τ

ϕ

ϕ ϕ

⋅

−=Γ

r shapefacto

*1

For practical purpose:

Material Models in SCC Mix Design

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